Finite Group DatabasebetaFinite Group DatabasebetaOrder 15296.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21439955 | C2 | semidirect |
| 2. #21439953 | C2 | semidirect |
| 3. #21439950 | C2 | semidirect |
| 4. #21439946 | C2 | semidirect |
| 5. #21439944 | C2 | semidirect |
| 6. #21439941 | C2 | semidirect |
| 7. #21439937 | C2 | semidirect |
| 9. C4×Dic478 | C2 | semidirect |
| 10. C4×C22⋊D239 | C2 | semidirect |
| 11. C4×C22⋊D239 | C2 | semidirect |
| 12. #21439919 | C2 | semidirect |
| 13. #21439917 | C2 | semidirect |
| 14. C2×C4×Dic239 | C2 | semidirect |
| 15. C4×D4×C239 | C2 | semidirect |
| 103. C239 | #529 | semidirect |
| 116. C4×D4 | D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21439955 | 2 |
| #21439953 | 2 |
| #21439950 | 2 |
| #21439946 | 2 |
| #21439944 | 2 |
| #21439941 | 2 |
| #21439937 | 2 |
| #21439932 | 2 |
| C4×Dic478 | 2 |
| C4×C22⋊D239 | 2 |
| #21439919 | 2 |
| #21439917 | 2 |
| C2×C4×Dic239 | 2 |
| C4×D4×C239 | 2 |
| #529 | 239 |